Hyperbolicity and astigmatism (Q5934435)

The main goal of this paper is to present some classes of chaotic high-dimensional billiards with all three types (focusing, dispersing and flat) components of the boundary. Moreover the author formulates the general approach to the construction of hyperbolic billiards in dimensions \(d\geq 3\) and to extend the notion of absolutely focusing mirrors to the higher dimensions. Furthermore the author presents some open problems and a new physical model inspired by the proof that defocusing works in \(d\geq 3\).